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Birkhäuser - Birkhäuser Mathematics | Plane Algebraic Curves - Translated by John Stillwell

Plane Algebraic Curves

Translated by John Stillwell

Brieskorn, Egbert, Knörrer, Horst

Translated by Stillwell, J.

Originally published 1981 as Ebene algebraische Kurven by Birkhäuser Boston

2012, X, 721 p. 301 illus.

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  • Lively introduction and overview of the field
  • Anchors the subject in history, science and technology
  • Clearly explains the tools from local analytic geometry and from algebraic and differential topology
  • Presents a wealth of attractive geometric illustrations ​

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the author’s concern for the student audience through emphasis upon motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles; this text provides a foundation for the comprehension and exploration of modern work on singularities.  

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In the first chapter one finds many special curves with very attractive geometric presentations – the wealth of illustrations is a distinctive characteristic of this book – and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book – and how else could it be with the first author – is the chapter on the resolution of singularities (always over the complex numbers).  (…) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject.

(Mathematical Reviews)

Content Level » Research

Keywords » Bézout's theorem - algebraic geometry - analytic geometry - projective geometry - resolution of singularities

Related subjects » Birkhäuser Mathematics

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